Free G-spaces and maximal equivariant compactifications

Abstract

For a compact Lie group G we prove that every free (resp., semifree) G-space admits a based-free (resp., semifree) G-compactification. Examples of finite- and infinite-dimensional G-spaces are presented that do not admit a free or based-free G-compactification. We give several characterizations of the maximal G-compactification beta X-G that are further applied to prove the formula (beta X-G)/H = beta(G/H)(X/H) for arbitrary closed normal subgroup H subset of G.